Prove the statistical distance between random variables

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Homework Help Overview

The original poster seeks assistance in proving the statistical distance between two random variables, X and Y. This involves understanding the concept of statistical distance in the context of probability distributions.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Some participants discuss the formula for statistical distance, referencing the maximum expected difference between the probability distributions of the random variables. Others may question the definitions or assumptions underlying the statistical distance.

Discussion Status

The discussion is ongoing, with participants sharing different aspects of the statistical distance concept. There is no explicit consensus yet, and the conversation appears to be exploring various interpretations and approaches to the problem.

Contextual Notes

There may be constraints related to the definitions of the random variables or the specific context in which the statistical distance is to be proven, which have not been fully articulated in the discussion.

bhenchodd
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Hi fellow members, I would appreciate if you could help with the following problem, it has had me stumped!

Prove the statistical distance between random variables X & Y

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Thank You, and have a great day!
 
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I know that dist(p, q) = max

maxEX |p(E)−q(E)| = p(E1)−q(E1) = q(E2)−p(E2);
dist(p, q) = p(E1) − q(E1) = q(E2) − p(E2).
 
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